CN111561930A - Method for restraining random drift error of vehicle-mounted MEMS gyroscope - Google Patents

Abstract

The invention discloses a method for suppressing random drift error of a vehicle-mounted MEMS gyroscope. The algorithm models and filters the output data of the on-board MEMS gyroscope sensor, so as to improve the accuracy and stability of the output data of the on-board MEMS gyroscope sensor. Aiming at the problem that there is a large error in the output data of the vehicle-mounted MEMS gyroscope sensor, the present invention firstly adopts the unit root test method to test the stability of the selected MEMS gyroscope output data. The change characteristics of the partial correlation coefficient map, and combined with the minimum information criterion, the time series ARMA model is constructed; then the ARMA model is applied to the discrete Kalman filter equation to obtain the filtered data; finally, the algorithm developed in this paper is verified by experiments. effectiveness. The method effectively suppresses the random error of the gyroscope and improves the signal-to-noise ratio of its output signal.

Description

A Method for Suppressing Random Drift Error of Vehicle-mounted MEMS Gyroscope

technical field

The invention relates to the technical field of MEMS gyroscope sensor application, in particular to a method for suppressing random drift error of a vehicle-mounted MEMS gyroscope.

Background technique

Micro Electro Mechanical Systems (MEMS) gyroscopes have the advantages of low cost, small size, light weight, low price, easy mass production, and integration, and are used in many different fields. Low-cost and low-precision MEMS gyroscopes are widely used in mobile phones, somatosensory game platforms and some wearable devices, which makes human-computer interaction reach new heights; mid-level MEMS gyroscope sensors are mainly used in industrial fields, such as electronic vehicle stabilization systems , GPS-assisted navigation, electronic stability control, medical equipment and other fields; in the military field, high-precision MEMS gyroscopes have a tendency to replace low-precision fiber-optic gyroscopes, which can meet the requirements of advanced equipment such as inertial GPS navigation and inertial guidance systems. .

Restricted by the manufacturing process and technical level, the measurement of low-cost MEMS inertial sensors currently contains large errors, which are divided into systematic errors and random errors. Systematic errors are generally caused by manufacturing or installation defects and can be calibrated by laboratory instruments; while random errors cannot be represented by a definite function expression, and need to be reduced by certain mathematical modeling and filtering compensation methods. influence of ... on.

和方差

如果|Xi-μ|＞kδ，则认为Xi附是粗大误差，并且用Xi附近的几个数据的平均值或中值代替。显然，上述μ和δ已经被过程中的潜在误差所影响，在一些情况下经常导致误判。除此之外，也有学者采用一阶高斯-马尔可夫随机误差建模方法对低成本MEMS陀螺仪输出数据进行误差建模，但该方法的自相关序列具有判定不精确的特点，且建模后需要进行一定的调整计算才可获得较为精确的模型，所以该方法在低成本MEMS陀螺仪随机误差建模的应用上并不广泛。In order to solve these problems, in recent years, many scholars have proposed to use wavelet algorithm theory and neural network modeling theory to deal with them. There are four most common rules for identifying random errors, namely the 3δ criterion, the Grubbs test, the Shawner criterion and the Dixon test. Without considering specific key factors and confidence levels, these four algorithms can be roughly described as: For a given set of samples {X1, X2,..., Xn}, calculate the sample mean

and variance

If |Xi-μ|>kδ, Xi is considered to be a gross error, and is replaced by the mean or median value of several data around Xi. Obviously, the above μ and δ have been affected by potential errors in the process, often leading to misjudgments in some cases. In addition, some scholars have used the first-order Gauss-Markov random error modeling method to model the error of the output data of the low-cost MEMS gyroscope, but the autocorrelation sequence of this method has the characteristics of inaccurate determination, and the modeling Afterwards, certain adjustments and calculations are required to obtain a more accurate model, so this method is not widely used in the random error modeling of low-cost MEMS gyroscopes.

Through the above analysis, it can be seen that the existing methods for dealing with random drift errors all have shortcomings. At the same time, there are relatively few research programs on the elimination of random drift errors of MEMS gyroscopes that can be put into use.

SUMMARY OF THE INVENTION

In order to overcome the shortcomings of the existing processing methods, reduce the random error of the output data of the low-cost MEMS gyroscope, and improve the signal-to-noise ratio of the output data, the purpose of the present invention is to provide a method for suppressing the random drift error of the vehicle-mounted MEMS gyroscope. The method has a simple modeling process, better modeling flexibility and stability, and can perform online filtering on the random error model of the MEMS gyroscope output data after modeling, which is suitable for consumer electronics, wearable devices, and medical equipment. , The improvement of the output data accuracy of MEMS gyroscope in the field of civil vehicle navigation.

For achieving the above object, the present invention adopts the following technical scheme:

A method for suppressing random drift error of a vehicle-mounted MEMS gyroscope, comprising the following steps:

Step 1, Construction of ARMA Model

Step 1.1, ADF inspection

When the time series satisfies the stationarity, the precondition for the autoregressive moving average model (ARMA) modeling of the time series is that after the MEMS gyroscope sequence is acquired in a static state, the Augmented Dickey-Fuller (ADF) is first used to model the MEMS gyroscope. The sequence is tested for stationarity. If the stationarity condition is met, go to step 1.2; if the stationarity condition is not met, difference calculation is required until it becomes a stationary time series;

其中

为自回归参数，ε(k)为均值为0，方差为σ²的白噪声序列，σ²为x(k)的方差；接着引入最小二乘法对自回归参数进行估计，即得到模型参数

的具体值；这一步中使AIC取得最小值的参数为最优参数，使AIC取得第二小的参数为次优参数；Firstly, the autocorrelation coefficient and partial correlation coefficient of x(k) are drawn. According to the distribution characteristics of ACF and PACF, combined with the minimum information criterion (AIC criterion), p, q determine the autoregressive moving average model suitable for x(k) as ARMA(1,0), the state equation is

in

is the autoregressive parameter, ε(k) is a white noise sequence with a mean value of 0 and a variance of ^σ2 , and ^σ2 is the variance of x(k); then the least squares method is introduced to estimate the autoregressive parameters, that is, the model parameters are obtained

The specific value of ; in this step, the parameter that makes AIC obtain the minimum value is the optimal parameter, and the parameter that makes AIC obtain the second smallest parameter is the sub-optimal parameter;

Step 1.3 Diagnose the model

为

定义残差为

如果模型拟合良好，模型的残差r(k)应该表现为白噪声，否则需要跳转到步骤1.2中，选择次优参数进行建模，若诊断图中没有明显的尖峰，则表示所选模型的拟合度好；In order to test whether the selected model is suitable for the data, it is necessary to carry out model diagnosis; according to the built ARAM(1,0) model, the predicted value of x(k) can be known

for

Define the residual as

If the model fits well, the residual r(k) of the model should appear as white noise. Otherwise, you need to jump to step 1.2 and select suboptimal parameters for modeling. If there is no obvious peak in the diagnostic graph, it means that the selected The fit of the model is good;

Step 2, Kalman filter compensation

Step 2.1 Build a mathematical model

According to the established ARMA(1,0) model, the system model of the Kalman filter equation is constructed as:

Among them, y(k) represents the k-th value of the stationary new sequence obtained after the difference of the MEMS gyroscope output sequence; w(k) is a white noise sequence with a mean value of 0 and a variance of σ ₂ , y(k)=x(k )+w(k) is the observation equation;

Step 2.2 Iterative Filtering

The filtering steps of the Kalman filter include time update and measurement update, that is, the output data of the gyroscope after the random error has been eliminated.

As an improvement, the stationarity test steps in step 1 are as follows: let the collected MEMS gyroscope data be data(t), t=1,2,...,n, where t represents the sampling sequence number, n represents the data length and is If it is a positive integer, perform ADF stationarity test on data(t). If it passes the stationarity test, go to step 1.2; ;

x(k)=data(k+1)-data(k) (1)

Among them, x(k) represents the time series of data(k) transformed by difference calculation, k=1,j+1,...,(n-1), j is the user-defined difference step size, for the difference sequence x (k) Perform ADF test until it satisfies the condition, at this time x(k) is a stationary sequence.

As an improvement, the time update and measurement update described in step 2.2 are as follows:

Time update:

State one-step prediction

One-step forecast error variance matrix

Measurement update:

Filter gain matrix K(k)=P(k,k-1)·[P(k,k-1)+σ] ^-1 ,

State estimation

Estimation error variance matrix P(k)=[1-K(k)]·P(k,k-1),

Among them, represents the one-step prediction value at time k obtained by recursion of the state equation, represents the one-step prediction error variance matrix at time k, represents the filter gain matrix at time k, represents the estimated value at time k, represents the estimation error at time k The variance matrix represents the matrix inversion operation; during the experiment, the initial value of P(k) in the Kalman filter is set to 0, and the initial value is set to 0.

After the Kalman filter processing, the random drift amplitude is significantly reduced, indicating that the Kalman filter can effectively suppress the disturbance information existing in the output data of the inertial device. By comparing the random data of the original MEMS gyroscope, after ARMA modeling, and after ARMA modeling combined with Kalman filtering, it is found that the mean value of random data processed by ARMA modeling combined with Kalman filtering method is closer to 0, and the variance is lower. It shows that the ARMA modeling combined with the Kalman filtering method introduced in this paper can effectively improve the stability and accuracy of the data, and has certain engineering practical value.

Beneficial effects:

Compared with the prior art, the present invention provides a method for suppressing the random drift error of a vehicle-mounted MEMS gyroscope. The method has the advantages of simple modeling process, high activity and strong stability, and can randomize the output data of the modeled MEMS gyroscope. The method for offline filtering processing of the error model is suitable for improving the accuracy of the output data of the MEMS gyroscope in the fields of consumer electronics, wearable equipment, medical equipment and civil vehicle navigation; The online filtering processing of the random error model of the output data can also reduce the random error of the output data of the low-cost MEMS gyroscope and improve the signal-to-noise ratio of the output data.

Description of drawings

Figure 1 is a comparison diagram of the original data and the first-order difference data, wherein (a) is the original data, and (b) is the data after the first-order difference;

Figure 2 is an ACF diagram of the differential data;

Figure 3 is a PACF diagram of the differential data;

Figure 4 is an ACF diagram of the residual;

Figure 5 is a PACF diagram of the residual;

FIG. 6 is a line graph of Kalman filter data.

Detailed ways

Example 1

A method for suppressing random drift error of a vehicle-mounted MEMS gyroscope, comprising the following steps:

Step 1, Construction of ARMA Model

Step 1.1, ADF inspection

The time series satisfying stationarity is the precondition for the autoregressive moving average model (ARMA) modeling of the time series. Therefore, after the MEMS gyroscope sequence is acquired in a static state, the Augmented Dickey-Fuller test (ADF) is used first to measure it. Carry out the stationarity test. If it meets the stationarity condition, go to step 1.2; if it does not meet the stationarity condition, it needs to be differentiated until it becomes a stationary time series.

Let the collected MEMS gyroscope data be data(t), t=1,2,...,n, where t represents the sampling number, n represents the data length and is a positive integer, and the ADF stationarity test is performed on data(t), If it passes the stationarity test, go to step 1.2; if not, enter the difference calculation for data(t) to obtain the stationary sequence x(k), and its calculation formula is:

x(k)=data(k+1)-data(k) (1)

Among them, x(k) represents the time series of data(k) transformed by difference calculation, k=1,j+1,...,(n-1), j is the user-defined difference step size, for the difference sequence x (k) Carry out the ADF test until it satisfies the conditions, at which time x(k) is a stationary sequence;

Step 1.2 Estimate ARMA(p,q) model parameters

其中

为自回归参数，ε(k)为均值为0，方差为σ²的白噪声序列，σ²为x(k)的方差；接着引入最小二乘法对自回归参数进行估计，即得到模型参数

的具体值；这一步中使AIC取得最小值的参数为最优参数，使AIC取得第二小的参数为次优参数；Firstly, the autocorrelation coefficient and partial correlation coefficient of x(k) are drawn. According to the distribution characteristics of ACF and PACF, combined with the minimum information criterion (AIC criterion), p, q determine the autoregressive moving average model suitable for x(k) as ARMA(1,0), the state equation is

in

is the autoregressive parameter, ε(k) is a white noise sequence with a mean value of 0 and a variance of ^σ2 , and ^σ2 is the variance of x(k); then the least squares method is introduced to estimate the autoregressive parameters, that is, the model parameters are obtained

The specific value of ; in this step, the parameter that makes AIC obtain the minimum value is the optimal parameter, and the parameter that makes AIC obtain the second smallest parameter is the sub-optimal parameter;

Step 1.3 Diagnose the model

In order to test whether the selected model fits the data, it is necessary to perform model diagnostics.

为

定义残差为

如果模型拟合良好，模型的残差r(k)应该表现为白噪声，否则需要跳转到步骤1.2中，选择次优参数进行建模，若诊断图中没有明显的尖峰，则表示所选模型的拟合度好。According to the established ARAM(1,0) model, the predicted value of x(k) can be known

for

Define the residual as

If the model fits well, the residual r(k) of the model should appear as white noise. Otherwise, you need to jump to step 1.2 and select suboptimal parameters for modeling. If there is no obvious peak in the diagnostic graph, it means that the selected The fit of the model is good.

Step 2 Kalman Filter Compensation

Step 2.1 Build a mathematical model

According to the established ARMA(1,0) model, the system model of the Kalman filter equation is constructed as:

Among them, y(k) represents the k-th value of the stationary new sequence obtained after the difference of the MEMS gyroscope output sequence; w(k) is a white noise sequence with 0 and a variance of σ ₂ ; y(k)=x(k)+ w(k) is the observation equation;

Step 2.2 Iterative Filtering

The filtering steps of the Kalman filter include time update and measurement update. The first two steps of the following recursive process are time update, and the last three steps are measurement update, as follows:

Time update:

state one-step prediction

One-step forecast error variance matrix

Measurement update:

Filter gain matrix K(k)=P(k,k-1)·[P(k,k-1)+σ] ^-1

State estimation

Estimation error variance matrix P(k)=[1-K(k)]·P(k,k-1)

表示利用状态方程递推得到的

在k时刻的一步预测值，P(k,k-1)表示k时刻的一步预测误差方差矩阵，K(k)表示k时刻的滤波增益矩阵，

表示x(k)在k时刻的估计值,P(k)表示k时刻的估计误差方差矩阵，[·]^-1表示矩阵求逆运算。实验过程中，卡尔曼滤波中的P(k)初值设定为0，

初值设定为0。in,

Represents obtained by recursion of the equation of state

The one-step prediction value at time k, P(k,k-1) represents the one-step prediction error variance matrix at time k, K(k) represents the filter gain matrix at time k,

Represents the estimated value of x(k) at time k, P(k) represents the estimated error variance matrix at time k, and [ ] ^-1 represents the matrix inversion operation. During the experiment, the initial value of P(k) in the Kalman filter is set to 0,

The initial value is set to 0.

After the Kalman filter processing, the random drift amplitude is significantly reduced, indicating that the Kalman filter can effectively suppress the disturbance information existing in the output data of the inertial device. By comparing the random data of the original MEMS gyroscope, after ARMA modeling, and after ARMA modeling combined with Kalman filtering, it is found that the mean value of random data processed by ARMA modeling combined with Kalman filtering method is closer to 0, and the variance is lower. It shows that the ARMA modeling combined with the Kalman filtering method introduced in this paper can effectively improve the stability and accuracy of the data, and has a high engineering practical value.

Example 2

In order to check the actual effect of the method for suppressing the random drift error of the vehicle-mounted MEMS gyroscope proposed by the present invention, a real vehicle experiment was carried out. The basic conditions of the experiment are described as follows:

The purpose of the experiment is to test the effect of the method for suppressing the random drift error of the vehicle-mounted MEMS gyroscope proposed by the present invention.

The composition of the experimental system: the experimental system is composed of software programs and hardware equipment. The processing program of the random drift error of the vehicle-mounted MEMS gyroscope is compiled according to the method for suppressing the random drift error of the vehicle-mounted MEMS gyroscope; the main hardware equipment includes: a computer (AMD TK-53CPU, 1G memory), Buick experiment Used car, Zhongxing Huanyu ZX-VG MEMS gyroscope, vehicle power inverter, PC-104 industrial computer.

Experimental setup: The gyroscope is fixed at the roof position where the Z-axis of the vehicle coordinate system passes in the positive direction, and the output data is saved in the PC-104 industrial computer.

Experiment route: A number of sports car experiments have been carried out on roads such as the Dingyuan Automobile Proving Ground of the General Equipment Department and the Nanjing Jiangning Development Zone.

Analysis of experimental results: Use Matlab to draw a line graph of the first 400 random data of the MEMS gyroscope's roll angular velocity (as shown in Figure 1(a)), and calculate the average value of the first 400 random data of the roll angular velocity. Its mean Mean1=-0.0977. Judging from the picture, the random data of the MEMS gyroscope at this time does not have the characteristics of zero mean, and the fluctuation is large. According to the ADF test, it is proved that the original data does not meet the requirements of stationarity. Therefore, it is necessary to perform a first-order difference on the first 400 data of the original MEMS gyroscope's roll angle and angular velocity, and draw 399 differential data line graphs after the difference (as shown in Figure 1(b)). Judging from the picture, the MEMS gyroscope after the difference The random data of the instrument is obviously stable before the score. Its mean Mean2=0.0096371, which is also closer to the zero mean sequence. Stochastic volatility is also more stable than pre-score. After the ADF test, it is proved that the differential MEMS gyroscope roll angle angular velocity sequence satisfies the zero-mean stationary sequence condition, so it can be used for time series analysis and modeling.

The differential MEMS gyroscope random data already has the requirement of stability, and Matlab can be used to draw the ACF graph (as shown in Figure 2) and PACF graph (as shown in Figure 3) of the first 399 MEMS gyroscope roll angle random data after the difference. Show). The autocorrelation coefficients and partial autocorrelation coefficients of the differential MEMS gyroscope output data have tailing characteristics, which are consistent with the modeling characteristics of the ARMA(p,q) model. It can be seen that the autoregressive order p=1,2, the moving average order q=0,1,2,3, the model AIC criterion, the model parameters are obtained by the least squares algorithm, the value of the AIC criterion under different orders is calculated, and the AIC is selected. The smallest model is used as a time series model. According to the principle that the smaller the AIC value, the higher the modeling accuracy, it is found that when p=1, q=0, the AIC achieves the minimum value, so the established model is the ARMA(1,0) model: x(k)=-0.5496x (k-1)+ε(k), where ε(k) represents a white noise sequence with mean 0 and variance 0.0143. After modeling, draw the ACF graph (as shown in Figure 4) and the PACF graph (as shown in Figure 5) of the residuals of the ARMA(1,0) model. Obviously, both the residual ACF and PACF maps have tailings, indicating that the fitted ARMA(1,0) model is reasonable and can be used for further filtering operations.

Bring the established ARMA(1,0) model into the Kalman filter system equation, we can get:

Then perform time update and measurement more recursion, the filtering result can be obtained as shown in Figure 6. By comparing the random data of the original MEMS gyroscope, after ARMA modeling, and after ARMA modeling combined with Kalman filtering, it is found that the mean value of random data processed by ARMA modeling combined with Kalman filtering method is closer to 0, and the variance is lower. It shows that the ARMA modeling combined with the Kalman filtering method introduced in the present invention can effectively improve the stability and accuracy of the data, and has a high engineering practical value.

The above are only preferred specific embodiments of the present invention, and the protection scope of the present invention is not limited thereto. Any person skilled in the art can obviously obtain the simplicity of the technical solution within the technical scope disclosed in the present invention. Variations or equivalent substitutions fall within the protection scope of the present invention.

Claims (3)

1. a method for suppressing the random drift error of a vehicle-mounted MEMS gyroscope, is characterized in that, comprises the steps: Step 1, Construction of ARMA Model Step 1.1, ADF inspection When the time series satisfies the stationarity, the precondition for the autoregressive moving average model ARMA modeling of the time series, after the MEMS gyroscope sequence is collected in a static state, the Augmented Dickey-Fuller is used to test the stationarity of the MEMS gyroscope sequence first. , if the stationarity condition is met, go to step 1.2; if the stationarity condition is not met, it needs to be differentially calculated until it becomes a stationary time series; let the obtained stationary sequence be x(t); Step 1.2 Estimate ARMA(p,q) model parameters First, make a graph of the autocorrelation coefficient and partial correlation coefficient of x(k). According to the distribution characteristics of ACF and PACF, combined with the AIC criterion, p, q determine the autoregressive moving average model suitable for x(k) as ARMA(1,0 ), the state equation is

in

is the autoregressive parameter, ε(k) is a white noise sequence with a mean value of 0 and a variance of ^σ2 , and ^σ2 is the variance of x(k); then the least squares method is introduced to estimate the autoregressive parameters, that is, the model parameters are obtained

The specific value of ; in this step, the parameter that makes AIC obtain the minimum value is the optimal parameter, and the parameter that makes AIC obtain the second smallest parameter is the sub-optimal parameter; Step 1.3 Diagnose the model In order to test whether the selected model is suitable for the data, it is necessary to carry out model diagnosis; according to the built ARAM(1,0) model, the predicted value of x(k) can be known

for

Define the residual as

If the model fits well, the residual r(k) of the model should appear as white noise. Otherwise, you need to jump to step 1.2 and select suboptimal parameters for modeling. If there is no obvious peak in the diagnostic graph, it means that the selected The fit of the model is good; Step 2, Kalman filter compensation Step 2.1 Build a mathematical model According to the established ARMA(1,0) model, the system model of the Kalman filter equation is constructed as:

Among them, y(k) represents the k-th value of the stationary new sequence obtained after the difference of the MEMS gyroscope output sequence; w(k) is a white noise sequence with a mean value of 0 and a variance of σ ² , y(k)=x(k )+w(k) is the observation equation; Step 2.2 Iterative Filtering The filtering steps of the Kalman filter include time update and measurement update, that is, the output data of the gyroscope after the random error has been eliminated. 2. the suppression method of a kind of vehicle-mounted MEMS gyroscope random drift error according to claim 1, it is characterized in that, in step 1, the step of checking the stability is as follows: set the MEMS gyroscope data collected to be data (t), t =1, 2, ..., n, where t represents the sampling sequence number, n represents the data length and is a positive integer, perform ADF stationarity test on data(t), if it passes the stationarity test, go to step 1.2; Then enter the difference calculation for data(t) to obtain the stationary sequence x(k), and its calculation formula is x(k)=data(k+1)-data(k) (1) Among them, x(k) represents the time series of data(k) transformed by difference calculation, k=1, j+1,..., (n-1), j is the user-defined difference step size, for the difference sequence x (k) Perform ADF test until it satisfies the condition, at this time x(k) is a stationary sequence. 3. the suppression method of a kind of vehicle-mounted MEMS gyroscope random drift error according to claim 1, is characterized in that, the time update described in the step 2.2 and the measurement update are specifically as follows: Time update: State one-step prediction

One-step forecast error variance matrix

Measurement update: Filter gain matrix K(k)=P(k, k-1)·[P(k, k-1)+σ] ^-1 , State estimation

Estimation error variance matrix P(k)=[1-K(k)]·P(k, k-1), Among them, represents the one-step prediction value at time k obtained by recursion of the state equation, represents the one-step prediction error variance matrix at time k, represents the filter gain matrix at time k, represents the estimated value at time k, represents the estimation error at time k The variance matrix represents the matrix inversion operation; during the experiment, the initial value of P(k) in the Kalman filter is set to 0, and the initial value is set to 0.

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